An auction website charges $1 for a bid. The bidding starts at 1¢ and goes up 1c at a time. A television that is worth
$2000 is won, on average, with a bid of $160. You make one bid at random.
Find the expected value of the outcome of the bid. (Write as an exact decimal, with a negative sign, if necessary.)
Expected Value: $

Respuesta :

The expected value of the outcome of the bid is $0.18

So let's start by counting how many bids are placed up to a total of 160.

100*160 = 16000.

What will be your arbitrary bid? As each bid has an equal chance of success, the average of all bids is used. (One cent plus 160 dollars) / 2 = 80 dollars (rounded)

Your odds of winning are 1/16000 (1 bid out of 16000).

If you win, your profit is 1920 ($2000 minus $80.00).

1920/16000 is $0.12

Your cost to enter the auction is $1, and your average winning offer is $0.12.

The result is $0.18 (0.12-1=-0.88).

Thus the expected value of the outcome of the bid is $0.18

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